Booking photos (mug shots) are used by law enforcement to aid in their investigations. These photos are, for the most part, accessible to the public as part of a public record and these photos are considered public domain material. There are few exceptions (ie. sealed records, ongoing investigation restrictions).
However, most media organizations will not use mug shots when illustrating a story unless or until the person photographed has been convicted of the crime for which he has been arrested. This is for several reasons. One reason is that a person who has been arrested for a crime may have been arrested in error or the arrest may never result in charges or a conviction. To publish a mug shot when there has been no conviction could potentially lead to a defamation action or an invasion of privacy/false light action against the publisher.
Studies have shown that mug shots imply guilt. The US Court of Appeals for the District of Columbia Circuit stated that a mug shot infers a criminal history and, therefore, a jury may infer guilt if they view a defendant's mug shot. Many courts in many states will instruct their attorneys not to use mug shots in court (or, if used, they should refrain from referring to them as mug shots).
In June, 1994, both Newsweek magazine and Time magazine chose O.J. Simpson's mug shot to illustrate their covers. Newsweek used the photograph as it was taken. Time magazine, however, hired a photo-illustrator to alter Simpson's mug shot photo, changing the background lighting and darkening Simpson's image.
Although Time editors claimed the image was darkened to convey that a "shadow" had fallen over the sport star's reputation, others viewed the darkening of O.J.'s face as racism. It was almost indisputable that the darkened image made Simpson appear more "menacing." What Time magazine did with the mug shot image was not illegal so much as it was unethical. Altering news photos is not something journalists should do. Time magazine noted the public's reaction to the cover and quickly removed the questionable issues from the news stands. The magazine replaced the cover mug shot photograph with another, more benign, photograph of Simpson.
Had you not been convicted of the misdemeanor under which you were arrested and charged, KTTNMD, you may have had some sort of legal action to consider against the arrest records website. As it stands, there is little you can do legally to have your mug shot removed from the website where it appears - and this would be the case, generally, whether the photograph has been altered or not. It could depend, I suppose, on how exactly the photo was altered.
Although you can certainly review the website and the facts of your situation with an attorney in your area, to get another opinion, I think your best (and perhaps only) action is the one you have already taken - request of the site that the mug shot be removed. As Proserpina said, it will not hurt to ask.